If Ailith takes 40 coins, then tells Hanna about the treasure chest and they split the remaining 60 coins equally, she will gain the maximum number of coins she could possibly carry in her backpack. Besides, she will share the treasure with Hanna without putting Hanna or herself in an awkward situation.

Notice that if Ailith takes more than 40 coins before including Hanna in this, she won't have enough incentive to claim at least half of the treasure and Hanna might suspect that there is something going on. The above solution is more likely to work with minimum risk of ruining the experience for Hanna since in sharing things that are not earned, often fairness is interpreted as equality.

Of course, this solution may seem a bit too selfish. It's just one possible solution. The aim was to look at the story as an optimization problem and play with the timing of the events rather than going one way or the other given the binary choices in the description.